Grade: 6 Unit: 1 Week: 4 Content: Math Dates: 9/10-9/14-12
Theme Essential Question: How do students connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems?
Essential Questions:
Can students use a model to show a percent?
Can students find the whole given a part of the percent?
Standards Ratios and Proportional Relationships 6.RP Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Objectives
The student will understand that a percent is rate per 100 and can be represented using tools such as tables of equivalent ratios, tape diagrams, double number line diagrams, and equations.
The student will understand that percentage-based rate problems compare two different units where one of the units is 100.
The student will understand that establishing connections between tools allow for extended reasoning and synthesis of the concept of ratios and rates (e.g., How do tape diagrams and double number lines show rate reasoning given the same context?).
Have students use advertisements to plan an imaginary shopping trip given a budget of various amounts. Students can create a poster showing the results of the shopping trip. www.lessonplanet.com imaginary shopping trip information
Key Questions
Can the student use a model to show percents and fractions?
Observable Student Behaviors
The student can writing a percent as a rate over 100.
The student can find the percent of a number using rate methods developed in 6.RP.3b.
Given the parts and a percent, the student can determine the whole.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary
Percent Ratios equivalent
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 6
Lessons 9-13, Pages 17-26
Teaching the Common Core Math Standards with Hands on Activities
Pg. 6-7
Mastering Common Core in Mathematics-Grade 6 (ABC)
Pg. 82-84, Ch. 6.8 and 6.9
Highly Recommended:
http://illustrativemathematics.org/illustrations/132 http://illustrativemathematics.org/illustrations/54 The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions. Gizmo Lessons
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.
Other Activities, etc. http://www.mathplayground.com/percent_shopping.html Solve 5 problems in each level. You select the toys which determines how challenging the activity will be. Level 1: Find the sale price when the original price and percent discount are known. Level 2: Find the percent discount when the original price and the sale price are known.
Big Math and Fries
http://illuminations.nctm.org/LessonDetail.aspx?id=L849 We are lucky to live in an age where there is a lot of nutrition information available for the food we eat. The problem is that much of the data is expressed in percents and some of those percents can be misleading. This lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.
Burning Questions
http://illuminations.nctm.org/LessonDetail.aspx?ID=L666 This is the culminating lesson for this unit. Students use information from a quiz, along with what they learned in the previous four lessons, to write a summary and finalize a property sketch. Students measure their own progress in a final activity by Testing Their Firewise IQ.
Burning Questions
http://illuminations.nctm.org/Lessons/OnFire/OnFire-AS-BurnQues.pdf This reproducible worksheet, from an Illuminations lesson, presents a series of questions with which students can test their knowledge of "firewise" landscaping and protecting their property from wildfires. The correct answers are provided on the second page.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L249 In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution. This lesson is adapted from "A Conceptual Model for Solving Percent Problems," which originally appeared in Mathematics Teaching in the Middle School, Vol. 1, No. 1 (April 1994), pp. 20-25.
How Steep Can You Be?
http://illuminations.nctm.org/LessonDetail.aspx?ID=L665 In this lesson, students consider the construction of a tool that will measure percent slope. They then use ideas about percent slope to determine recommended defensible space distances near a home.
http://illuminations.nctm.org/LessonDetail.aspx?ID=U99 Students participate in activities in which they develop number sense in and around the shopping mall. The first lesson in this unit is appropriate for grades 3 - 5, and the second lesson is appropriate for grades 6 - 8. Both grade-level activities deal with size and space, estimation, measurement, and applications involving percent. This unit was adapted from an article entitled "Mathematics at the Mall," written by Francis Fennell, which appeared in Teaching Children Mathematics, January, 1998, vol.4, no.5, pp. 268 – 274.
Theme Essential Question: How do students connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems?
Essential Questions:
Standards
Ratios and Proportional Relationships 6.RP
Understand ratio concepts and use ratio reasoning to solve problems.
Objectives
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
http://www.azed.gov/standards-practices/files/2011/06/2010mathgr6.pdf
Ohio Dept of Education Mathematics Model Curriculum 6-28-2011
Assessment
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Ratios
equivalent
Suggested Activities [see Legend to highlight MCO and HYS]
- Houghton Mifflin OnCore Mathematics Middle School Grade 6
- Lessons 9-13, Pages 17-26
- Teaching the Common Core Math Standards with Hands on Activities
- Pg. 6-7
- Mastering Common Core in Mathematics-Grade 6 (ABC)
- Pg. 82-84, Ch. 6.8 and 6.9
- Highly Recommended:
http://illustrativemathematics.org/illustrations/132http://illustrativemathematics.org/illustrations/54
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Gizmo Lessons
- Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.Diverse Learners:
Homework
Terminology for Teachers
A percent is a ratio that compares a number to 100. It represents part of a whole.
Resources
Professional Texts
Literary Texts
Informational Texts
Art, Music, and Media
Manipulatives
Games
Videos
Websites
SMART Board Lessons, Promethean Lessons
Other Activities, etc.
http://www.mathplayground.com/percent_shopping.html Solve 5 problems in each level. You select the toys which determines how challenging the activity will be. Level 1: Find the sale price when the original price and percent discount are known.
Level 2: Find the percent discount when the original price and the sale price are known.
- Big Math and Fries
http://illuminations.nctm.org/LessonDetail.aspx?id=L849We are lucky to live in an age where there is a lot of nutrition information available for the food we eat. The problem is that much of the data is expressed in percents and some of those percents can be misleading. This lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.
- Burning Questions
http://illuminations.nctm.org/LessonDetail.aspx?ID=L666This is the culminating lesson for this unit. Students use information from a quiz, along with what they learned in the previous four lessons, to write a summary and finalize a property sketch. Students measure their own progress in a final activity by Testing Their Firewise IQ.
- Burning Questions
http://illuminations.nctm.org/Lessons/OnFire/OnFire-AS-BurnQues.pdfThis reproducible worksheet, from an Illuminations lesson, presents a series of questions with which students can test their knowledge of "firewise" landscaping and protecting their property from wildfires. The correct answers are provided on the second page.
- Creating an Effective Defensible Space
http://illuminations.nctm.org/Lessons/OnFire/OnFire-LWF-DefenSpace.pdfThis reproducible handout, from an Illuminations lesson, offers step-by-step instructions for creating an effective defensible space to protect your home from wildfires.
- Grid and Percent It
http://illuminations.nctm.org/LessonDetail.aspx?ID=L249In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution. This lesson is adapted from "A Conceptual Model for Solving Percent Problems," which originally appeared in Mathematics Teaching in the Middle School, Vol. 1, No. 1 (April 1994), pp. 20-25.
- How Steep Can You Be?
http://illuminations.nctm.org/LessonDetail.aspx?ID=L665In this lesson, students consider the construction of a tool that will measure percent slope. They then use ideas about percent slope to determine recommended defensible space distances near a home.
- How Steep Can You Be?
http://illuminations.nctm.org/Lessons/OnFire/OnFire-AS-Steep.pdfThis reproducible activity sheet, from an Illuminations lesson, walks students through the process of creating defensible space around a building on a chosen piece of property
- Percent Slope Tool
http://illuminations.nctm.org/Lessons/OnFire/OnFire-AS-PerSlopeTool.pdfThis reproducible activity, from an Illuminations lesson, provides a template by which students can create a tool for calculating the slope of real-world inclines.
- Shopping Mall Math Unit
http://illuminations.nctm.org/LessonDetail.aspx?ID=U99Students participate in activities in which they develop number sense in and around the shopping mall. The first lesson in this unit is appropriate for grades 3 - 5, and the second lesson is appropriate for grades 6 - 8. Both grade-level activities deal with size and space, estimation, measurement, and applications involving percent. This unit was adapted from an article entitled "Mathematics at the Mall," written by Francis Fennell, which appeared in Teaching Children Mathematics, January, 1998, vol.4, no.5, pp. 268 – 274.
- Shops at the Mall
http://illuminations.nctm.org/LessonDetail.aspx?ID=L266Students participate in an activity in which they develop number sense in and around the shopping mall. They solve problems involving percent and scale drawings.
Language
Arts
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Week 3
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Week 5
Week 6
6 Matrix
6 PAP Matrix
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Week 2
Week 3
Week 4
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Week 6
Home K-2
Home 3-5
Home 6-8
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Unit 4
Unit 5
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